Does Blender downgrade textures?
Blender doesn't change the textures in any way by itself and this applies to all possible actions. 

The texture size does not necessarily define its quality, it depends on the source (image texture, procedural material, tiling, up/donwscaling...) but normally I'd say that everything from 1k upwards is fine.

You might want to check Blender's System Settings. Hit Ctrl+Alt+U, go to "System" and play around with the settings for "Mipmap" and "Anisotropic Filtering". Deactivating them seems to help in many cases.